TSTP Solution File: GRP184-4 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP184-4 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n032.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 11:46:12 EDT 2022
% Result : Unsatisfiable 0.14s 0.39s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 17
% Syntax : Number of clauses : 48 ( 48 unt; 0 nHn; 48 RR)
% Number of literals : 48 ( 0 equ; 16 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(inverse(identity),identity),
file('GRP184-4.p',unknown),
[] ).
cnf(2,axiom,
equal(inverse(inverse(u)),u),
file('GRP184-4.p',unknown),
[] ).
cnf(3,axiom,
equal(inverse(multiply(u,v)),multiply(inverse(v),inverse(u))),
file('GRP184-4.p',unknown),
[] ).
cnf(4,axiom,
equal(least_upper_bound(inverse(u),inverse(v)),inverse(greatest_lower_bound(u,v))),
file('GRP184-4.p',unknown),
[] ).
cnf(5,axiom,
equal(inverse(least_upper_bound(u,v)),greatest_lower_bound(inverse(u),inverse(v))),
file('GRP184-4.p',unknown),
[] ).
cnf(6,axiom,
~ equal(multiply(least_upper_bound(a,identity),inverse(greatest_lower_bound(a,identity))),multiply(inverse(greatest_lower_bound(a,identity)),least_upper_bound(a,identity))),
file('GRP184-4.p',unknown),
[] ).
cnf(7,axiom,
equal(multiply(identity,u),u),
file('GRP184-4.p',unknown),
[] ).
cnf(8,axiom,
equal(multiply(inverse(u),u),identity),
file('GRP184-4.p',unknown),
[] ).
cnf(10,axiom,
equal(greatest_lower_bound(u,v),greatest_lower_bound(v,u)),
file('GRP184-4.p',unknown),
[] ).
cnf(11,axiom,
equal(least_upper_bound(u,v),least_upper_bound(v,u)),
file('GRP184-4.p',unknown),
[] ).
cnf(12,axiom,
equal(greatest_lower_bound(greatest_lower_bound(u,v),w),greatest_lower_bound(u,greatest_lower_bound(v,w))),
file('GRP184-4.p',unknown),
[] ).
cnf(16,axiom,
equal(least_upper_bound(u,greatest_lower_bound(u,v)),u),
file('GRP184-4.p',unknown),
[] ).
cnf(17,axiom,
equal(greatest_lower_bound(u,least_upper_bound(u,v)),u),
file('GRP184-4.p',unknown),
[] ).
cnf(18,axiom,
equal(multiply(u,least_upper_bound(v,w)),least_upper_bound(multiply(u,v),multiply(u,w))),
file('GRP184-4.p',unknown),
[] ).
cnf(19,axiom,
equal(multiply(u,greatest_lower_bound(v,w)),greatest_lower_bound(multiply(u,v),multiply(u,w))),
file('GRP184-4.p',unknown),
[] ).
cnf(20,axiom,
equal(multiply(least_upper_bound(u,v),w),least_upper_bound(multiply(u,w),multiply(v,w))),
file('GRP184-4.p',unknown),
[] ).
cnf(21,axiom,
equal(multiply(greatest_lower_bound(u,v),w),greatest_lower_bound(multiply(u,w),multiply(v,w))),
file('GRP184-4.p',unknown),
[] ).
cnf(22,plain,
~ equal(least_upper_bound(multiply(inverse(greatest_lower_bound(identity,a)),identity),multiply(inverse(greatest_lower_bound(identity,a)),a)),least_upper_bound(inverse(greatest_lower_bound(identity,a)),multiply(a,inverse(greatest_lower_bound(identity,a))))),
inference(rew,[status(thm),theory(equality)],[7,6,20,18,10,11]),
[iquote('0:Rew:7.0,6.0,20.0,6.0,18.0,6.0,10.0,6.0,11.0,6.0')] ).
cnf(32,plain,
equal(multiply(u,inverse(u)),identity),
inference(spr,[status(thm),theory(equality)],[2,8]),
[iquote('0:SpR:2.0,8.0')] ).
cnf(44,plain,
equal(greatest_lower_bound(u,least_upper_bound(v,u)),u),
inference(spr,[status(thm),theory(equality)],[11,17]),
[iquote('0:SpR:11.0,17.0')] ).
cnf(64,plain,
equal(greatest_lower_bound(greatest_lower_bound(u,v),u),greatest_lower_bound(u,v)),
inference(spr,[status(thm),theory(equality)],[16,44]),
[iquote('0:SpR:16.0,44.0')] ).
cnf(66,plain,
equal(greatest_lower_bound(u,greatest_lower_bound(u,v)),greatest_lower_bound(u,v)),
inference(rew,[status(thm),theory(equality)],[10,64]),
[iquote('0:Rew:10.0,64.0')] ).
cnf(90,plain,
equal(least_upper_bound(inverse(u),inverse(v)),inverse(greatest_lower_bound(v,u))),
inference(spr,[status(thm),theory(equality)],[4,11]),
[iquote('0:SpR:4.0,11.0')] ).
cnf(95,plain,
equal(least_upper_bound(inverse(u),v),inverse(greatest_lower_bound(u,inverse(v)))),
inference(spr,[status(thm),theory(equality)],[2,4]),
[iquote('0:SpR:2.0,4.0')] ).
cnf(101,plain,
equal(inverse(greatest_lower_bound(u,v)),inverse(greatest_lower_bound(v,u))),
inference(rew,[status(thm),theory(equality)],[4,90]),
[iquote('0:Rew:4.0,90.0')] ).
cnf(104,plain,
~ equal(least_upper_bound(multiply(inverse(greatest_lower_bound(identity,a)),identity),multiply(inverse(greatest_lower_bound(identity,a)),a)),inverse(greatest_lower_bound(greatest_lower_bound(identity,a),inverse(multiply(a,inverse(greatest_lower_bound(identity,a))))))),
inference(rew,[status(thm),theory(equality)],[95,22]),
[iquote('0:Rew:95.0,22.0')] ).
cnf(108,plain,
~ equal(least_upper_bound(multiply(inverse(greatest_lower_bound(identity,a)),identity),multiply(inverse(greatest_lower_bound(identity,a)),a)),inverse(greatest_lower_bound(identity,greatest_lower_bound(a,inverse(multiply(a,inverse(greatest_lower_bound(identity,a)))))))),
inference(rew,[status(thm),theory(equality)],[12,104]),
[iquote('0:Rew:12.0,104.0')] ).
cnf(170,plain,
equal(least_upper_bound(u,v),inverse(greatest_lower_bound(inverse(u),inverse(v)))),
inference(spr,[status(thm),theory(equality)],[5,2]),
[iquote('0:SpR:5.0,2.0')] ).
cnf(192,plain,
~ equal(inverse(greatest_lower_bound(inverse(multiply(inverse(greatest_lower_bound(identity,a)),identity)),inverse(multiply(inverse(greatest_lower_bound(identity,a)),a)))),inverse(greatest_lower_bound(identity,greatest_lower_bound(a,inverse(multiply(a,inverse(greatest_lower_bound(identity,a)))))))),
inference(rew,[status(thm),theory(equality)],[170,108]),
[iquote('0:Rew:170.0,108.0')] ).
cnf(226,plain,
~ equal(inverse(greatest_lower_bound(multiply(inverse(identity),inverse(inverse(greatest_lower_bound(identity,a)))),multiply(inverse(a),inverse(inverse(greatest_lower_bound(identity,a)))))),inverse(greatest_lower_bound(identity,greatest_lower_bound(a,inverse(multiply(a,inverse(greatest_lower_bound(identity,a)))))))),
inference(rew,[status(thm),theory(equality)],[3,192]),
[iquote('0:Rew:3.0,192.0,3.0,192.0')] ).
cnf(227,plain,
~ equal(inverse(greatest_lower_bound(greatest_lower_bound(identity,a),multiply(inverse(a),greatest_lower_bound(identity,a)))),inverse(greatest_lower_bound(identity,greatest_lower_bound(a,inverse(multiply(a,inverse(greatest_lower_bound(identity,a)))))))),
inference(rew,[status(thm),theory(equality)],[7,226,1,2]),
[iquote('0:Rew:7.0,226.0,1.0,226.0,2.0,226.0')] ).
cnf(228,plain,
~ equal(inverse(greatest_lower_bound(identity,greatest_lower_bound(a,greatest_lower_bound(multiply(inverse(a),identity),multiply(inverse(a),a))))),inverse(greatest_lower_bound(identity,greatest_lower_bound(a,inverse(multiply(a,inverse(greatest_lower_bound(identity,a)))))))),
inference(rew,[status(thm),theory(equality)],[12,227,19]),
[iquote('0:Rew:12.0,227.0,19.0,227.0')] ).
cnf(229,plain,
~ equal(inverse(greatest_lower_bound(identity,greatest_lower_bound(a,greatest_lower_bound(identity,multiply(inverse(a),identity))))),inverse(greatest_lower_bound(identity,greatest_lower_bound(a,inverse(multiply(a,inverse(greatest_lower_bound(identity,a)))))))),
inference(rew,[status(thm),theory(equality)],[10,228,8]),
[iquote('0:Rew:10.0,228.0,8.0,228.0')] ).
cnf(240,plain,
equal(multiply(inverse(u),identity),inverse(multiply(identity,u))),
inference(spr,[status(thm),theory(equality)],[1,3]),
[iquote('0:SpR:1.0,3.0')] ).
cnf(245,plain,
equal(inverse(multiply(u,inverse(v))),multiply(v,inverse(u))),
inference(spr,[status(thm),theory(equality)],[2,3]),
[iquote('0:SpR:2.0,3.0')] ).
cnf(250,plain,
equal(multiply(inverse(u),identity),inverse(u)),
inference(rew,[status(thm),theory(equality)],[7,240]),
[iquote('0:Rew:7.0,240.0')] ).
cnf(251,plain,
~ equal(inverse(greatest_lower_bound(identity,greatest_lower_bound(a,inverse(multiply(a,inverse(greatest_lower_bound(identity,a))))))),inverse(greatest_lower_bound(identity,greatest_lower_bound(a,greatest_lower_bound(identity,inverse(a)))))),
inference(rew,[status(thm),theory(equality)],[250,229]),
[iquote('0:Rew:250.0,229.0')] ).
cnf(315,plain,
equal(greatest_lower_bound(greatest_lower_bound(u,v),w),greatest_lower_bound(v,greatest_lower_bound(u,w))),
inference(spr,[status(thm),theory(equality)],[10,12]),
[iquote('0:SpR:10.0,12.0')] ).
cnf(321,plain,
equal(greatest_lower_bound(u,greatest_lower_bound(v,w)),greatest_lower_bound(v,greatest_lower_bound(u,w))),
inference(rew,[status(thm),theory(equality)],[12,315]),
[iquote('0:Rew:12.0,315.0')] ).
cnf(322,plain,
~ equal(inverse(greatest_lower_bound(identity,greatest_lower_bound(a,inverse(multiply(a,inverse(greatest_lower_bound(identity,a))))))),inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,greatest_lower_bound(a,inverse(a)))))),
inference(rew,[status(thm),theory(equality)],[321,251]),
[iquote('0:Rew:321.0,251.0')] ).
cnf(332,plain,
~ equal(inverse(greatest_lower_bound(identity,greatest_lower_bound(a,inverse(multiply(a,inverse(greatest_lower_bound(identity,a))))))),inverse(greatest_lower_bound(identity,greatest_lower_bound(a,inverse(a))))),
inference(rew,[status(thm),theory(equality)],[66,322]),
[iquote('0:Rew:66.0,322.0')] ).
cnf(906,plain,
equal(inverse(multiply(u,inverse(greatest_lower_bound(v,w)))),multiply(greatest_lower_bound(w,v),inverse(u))),
inference(spr,[status(thm),theory(equality)],[101,245]),
[iquote('0:SpR:101.0,245.0')] ).
cnf(953,plain,
equal(inverse(multiply(u,inverse(greatest_lower_bound(v,w)))),greatest_lower_bound(multiply(w,inverse(u)),multiply(v,inverse(u)))),
inference(rew,[status(thm),theory(equality)],[21,906]),
[iquote('0:Rew:21.0,906.0')] ).
cnf(954,plain,
~ equal(inverse(greatest_lower_bound(identity,greatest_lower_bound(a,greatest_lower_bound(multiply(a,inverse(a)),multiply(identity,inverse(a)))))),inverse(greatest_lower_bound(identity,greatest_lower_bound(a,inverse(a))))),
inference(rew,[status(thm),theory(equality)],[953,332]),
[iquote('0:Rew:953.0,332.0')] ).
cnf(972,plain,
~ equal(inverse(greatest_lower_bound(identity,greatest_lower_bound(a,greatest_lower_bound(identity,inverse(a))))),inverse(greatest_lower_bound(identity,greatest_lower_bound(a,inverse(a))))),
inference(rew,[status(thm),theory(equality)],[32,954,7]),
[iquote('0:Rew:32.0,954.0,7.0,954.0')] ).
cnf(973,plain,
~ equal(inverse(greatest_lower_bound(identity,greatest_lower_bound(identity,greatest_lower_bound(a,inverse(a))))),inverse(greatest_lower_bound(identity,greatest_lower_bound(a,inverse(a))))),
inference(rew,[status(thm),theory(equality)],[321,972]),
[iquote('0:Rew:321.0,972.0')] ).
cnf(974,plain,
~ equal(inverse(greatest_lower_bound(identity,greatest_lower_bound(a,inverse(a)))),inverse(greatest_lower_bound(identity,greatest_lower_bound(a,inverse(a))))),
inference(rew,[status(thm),theory(equality)],[66,973]),
[iquote('0:Rew:66.0,973.0')] ).
cnf(975,plain,
$false,
inference(obv,[status(thm),theory(equality)],[974]),
[iquote('0:Obv:974.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : GRP184-4 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.00/0.10 % Command : run_spass %d %s
% 0.09/0.29 % Computer : n032.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 600
% 0.09/0.29 % DateTime : Mon Jun 13 10:42:41 EDT 2022
% 0.09/0.30 % CPUTime :
% 0.14/0.39
% 0.14/0.39 SPASS V 3.9
% 0.14/0.39 SPASS beiseite: Proof found.
% 0.14/0.39 % SZS status Theorem
% 0.14/0.39 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.39 SPASS derived 631 clauses, backtracked 0 clauses, performed 0 splits and kept 157 clauses.
% 0.14/0.39 SPASS allocated 64084 KBytes.
% 0.14/0.39 SPASS spent 0:00:00.09 on the problem.
% 0.14/0.39 0:00:00.03 for the input.
% 0.14/0.39 0:00:00.00 for the FLOTTER CNF translation.
% 0.14/0.39 0:00:00.00 for inferences.
% 0.14/0.39 0:00:00.00 for the backtracking.
% 0.14/0.39 0:00:00.04 for the reduction.
% 0.14/0.39
% 0.14/0.39
% 0.14/0.39 Here is a proof with depth 2, length 48 :
% 0.14/0.39 % SZS output start Refutation
% See solution above
% 0.14/0.40 Formulae used in the proof : p21x_1 p21x_2 p21x_3 p21x_4 p21x_5 prove_p21x left_identity left_inverse symmetry_of_glb symmetry_of_lub associativity_of_glb lub_absorbtion glb_absorbtion monotony_lub1 monotony_glb1 monotony_lub2 monotony_glb2
% 0.14/0.40
%------------------------------------------------------------------------------